TFS forms can only be modified at design time.
The TFS forms engine is capable of specifying different layouts for different targets, which already tells us that it is a subset of the rendering engines for those targets, and as far as I know, with less capabilities. One of the restrictions is exactly that forms can only be modified at design time.
As a workaround, at the bottom of the page on how to specify work item form controls, there is a link to an article on how to implement a custom control using Winforms. It might be possible to create a custom control with multiple drop down boxes which are dynamically displayed; I have not yet tried that.
You can get better samples on how to implement a custom control in the Custom Controls for TFS Work Item Tracking project at CodePlex. The challenge though will be to also generate a web implementation for the same control, otherwise your work items will be visible only from Team Explorer.